Page 123 - Multidimensional Chromatography

Coupled-Column Liquid Chromatography 115

Differentiation of equation (5.12), with respect to , as above, shows the maxi-
mum to occur at 1/2, and then the maximum S/ ratio can be estimated by the
following equation:

(S/ ) max 0.5 exp( 1) 0.1839 (5.14)

which leads to the fact that only about 18% of the analytes will emerge as single-
component peaks.
The above theoretical analysis of the total number of resolvable components in a
complex mixture has shown that in LC, relative to the maximum peak content or
peak capacity for closely spaced peaks, a random chromatogram will never contain
more than about 37% of its potential peaks and furthermore that only 18% of such
components will emerge as single-component peaks having a minimum specified
resolution with respect to the neighbouring peaks.
A practical method for enhancing the peak capacity, and thus the resolution of
analytes in multicomponent complex mixtures, can be achieved by changing the
mode of the separation during the chromatographic analysis, employing a column
switching system in order to optimize a separation.
In LC–LC coupling (2D system), the peak capacity is the product of the peak
capacities of its component one-dimensional (1D) processes (9). The power of the
separation measured by the LC–LC peak capacity is given by the following:

(5.15)
LC – LC LC1 LC2
By assuming that both LC modes have the same peak capacity, equation (5.15)
becomes:

LC – LC 2 (5.16)

More generally the peak capacity for a multidimensional system can be expressed by
the following:
n
(5.17)
1 2 3

n i
and assuming that each LC mode has the same peak capacity, equation 5.17 can con-
veniently be expressed as follows:

n (5.18)

On the other hand, supposing that we have n identical columns connected in series,
the peak capacity is given, in analogy to equation 5.3, by the following expression
(10):
(nN) 1/2
S 1 ln(1 k n ) (5.19)
r